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Pretty much all Nim games can be solved by starting at the end and working backwards. Let's first solve the basic Nim, with only one pile, and simple actions (take 1-4). Let's enumerate the endgame situations by how many sticks are left, and see what kind of pattern emerges: Rules: 2 players, one pile, take 1-4, taking last wins 0: loss, cannot take 1: ...


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